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A linear circuit is one that has no nonlinear electronic components in it. [1] [2] [3] Examples of linear circuits are amplifiers, differentiators, and integrators, linear electronic filters, or any circuit composed exclusively of ideal resistors, capacitors, inductors, op-amps (in the "non-saturated" region), and other "linear" circuit elements.
Circuits with only linear elements, linear circuits, do not cause intermodulation distortion and can be easily analysed with powerful mathematical techniques such as the Laplace transform. Nonlinear elements – these are elements in which the relation between voltage and current is a nonlinear function .
Although the gyrator was conceived as a fifth linear element, its adoption makes both the ideal transformer and either the capacitor or inductor redundant. Thus the number of necessary linear elements is in fact reduced to three. Circuits that function as gyrators can be built with transistors and op-amps using feedback.
The points where the characteristic curve and the load line intersect are the possible operating point(s) of the circuit; at these points the current and voltage parameters of both parts of the circuit match. [1] The example at right shows how a load line is used to determine the current and voltage in a simple diode circuit.
If all circuit components were linear or the circuit was linearized beforehand, the equation system at this point is a system of linear equations and is solved with numerical linear algebra methods. Otherwise, it is a nonlinear algebraic equation system and is solved with nonlinear numerical methods such as Root-finding algorithms.
To design any electrical circuit, either analog or digital, electrical engineers need to be able to predict the voltages and currents at all places within the circuit. [1] Linear circuits, that is, circuits wherein the outputs are linearly dependent on the inputs, can be analyzed by hand using complex analysis. Simple nonlinear circuits can ...
Mathematical Methods in Electronics Engineering involves applying mathematical principles to analyze, design, and optimize electronic circuits and systems. Key areas include: [1] [2] Linear Algebra: Used to solve systems of linear equations that arise in circuit analysis. Applications include network theory and the analysis of electrical ...
Many of the electrical components used in simple electric circuits, such as resistors, inductors, and capacitors are linear. [citation needed] Circuits made with these components, called linear circuits, are governed by linear differential equations, and can be solved easily with powerful mathematical frequency domain methods such as the Laplace transform.